Closed-loop multiple-input-multiple-output scheme for wireless communication based on hierarchical feedback

ABSTRACT

The present invention provides methods implemented in a base station having a plurality of antennas and one or more user terminals. One embodiment of the method includes receiving feedback from at least one user in response to transmitting a first frame to said at least one user. The first frame is formed by pre-coding at least one symbol using at least one first code word selected from at least one first code book associated with the at least one user. The method also includes transmitting at least one second frame to the user(s). The second frame(s) are pre-coded using at least one second codeword selected from at least one second codebook. The second codebook(s) determined based on the feedback and the first codeword(s).

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to communication systems, and, moreparticularly, to wireless communication systems.

2. Description of the Related Art

Base stations in wireless communication systems provide wirelessconnectivity to users within the geographic area, or cell, associatedwith the base station. The wireless communication links between the basestation and each of the users typically include one or more downlink (orforward) channels for transmitting information from the base station tothe mobile unit and one or more uplink (or reverse) channels fortransmitting information from the mobile unit to the base station.Multiple-input-multiple-output (MIMO) techniques may be employed whenthe base station and, optionally, the user terminals include multipleantennas. For example, a base station that includes multiple antennascan transmit multiple independent and distinct signals to multiple usersconcurrently and on the same frequency band. MIMO techniques are capableof increasing the spectral efficiency of the wireless communicationsystem roughly in proportion to the number of antennas available at thebase station. However, the base station also requires information aboutthe state of the downlink channel(s) to each of the users to selectusers that have approximately orthogonal downlink channels forconcurrent transmission. The channel feedback may be provided by theusers on the reverse link, but this increases overhead associated withthe MIMO transmissions, which reduces the spectral efficiency of thewireless communication system.

Random fluctuations in the channel states can create sets of downlinkchannels that are approximately orthogonal. Thus, if the number of usersassociated with a base station is large, these random fluctuationsnaturally tend to create groups of users that have approximatelyorthogonal downlink channels. Opportunistic MIMO schemes identify thesegroups of users so that the interference between the concurrenttransmissions from the base station to the users in the selected groupis within an acceptable tolerance level. For example, let n_(T) denotethe number of transmit antennas at the base station and let K indicatethe number of users connected to the base station. Each user is equippedwith n_(R) receive antennas. The channel coefficients between eachtransmit antenna and each receive antenna at user k can be assembledinto an n_(R)×n_(T) matrix H_(k), k=1, . . . , K.

In a multi-user MIMO system that employs linear pre-coding matrices, thebase station can transmit concurrently to as many as n_(T) users, whichcan be chosen from the population of K users. The relationship betweentransmit and receive signals can be represented as:

y=HGd+n

where d is an n_(T)-dimensional vector containing the transmit symbols,y is the n_(R)-dimensional vector of received signals, n is ann_(R)-dimensional noise vector, and G is an n_(T)×n_(T) pre-codingmatrix. Note that some of the entries of d may be zero if the basestation chooses to transmit to less than n_(T) users (this is sometimestermed “rank adaptation”). The mobile units and the base station alsostore copies of a codebook consisting of L quantization matrices, C_(i),i=1, . . . , L, which are used to quantize information for transmission.Altogether, the L quantization matrices amount to n_(T)·L columnvectors, where each column vector has n_(T) entries. Each mobile unitquantizes its single user channel direction to the codeword of thecodebook that maximizes a given criterion. At the mobile side, scalar orvector quantization can be used.

The base station can generate the pre-coding matrices based on itsknowledge of the matrices H_(k), k=1, . . . , K. However, this knowledgeis typically incomplete because the transmitter at the base station isnot able to determine the exact values of the channel matrices H_(k).The base station must therefore rely on feedback from each mobile unitthat reports an estimate the mobile unit's single-user channel matrixH_(k). For example, when the base station implements an opportunisticscheme, each user periodically reports channel direction informationthat includes information indicating a preferred subset of the columnvectors (or code words) in the codebook of L quantization matrices,C_(i), i=1, . . . , L. The channel direction information is reported viathe reverse link to the base station. The users also report a qualityindicator corresponding to a hypothetical transmission associated witheach preferred column. The base station can then generate precodingmatrices using the channel direction information provided by the mobileunits.

A general solution for the optimal vector quantizer that maximizes themutual information in a MIMO multi-user transmission is not known. Love,et al (“Grassmannian beamforming for multiple-input multiple-outputwireless systems,” IEEE Trans. Inf. Theory, vol. 49, no. 10, pp.2735-2747, October 2003) have demonstrated that the problem ofmaximizing the throughput for a MIMO single-user system with limitedfeedback is equivalent to the problem of packing one dimensionalsubspace known as Grassmannian line packing. However, this approach hasnot been extended to the multi-user case and in particular to zeroforcing (ZF) based scheme.

Santipath and Honig (“Asymptotic capacity of beamforming with limitedfeedback,” in IEEE Int. Symp. Info. Theory, Chicago, Ill., USA, July2004, “Signature optimisation for CDMA with limited feedback,” IEEETrans. Inf. Theory, vol. 51, no. 10, pp. 3475-3492, October 2005)describe random vector quantization (RVQ) techniques. In RVQ techniques,quantization codewords are independently chosen from an isotropicdistribution on an M-dimensional unit sphere, where M is the number oftransmit antennas. The RVQ approach provides an estimate of the lowerbound of the performance of a quantization scheme because any reasonablywell-designed codebook should perform at least as well as RVQ. When thenumber of feedback bits is small, the lower bound could be very loosebecause a RVQ codebook does not uniformly cover the M-dimensional space.

Philips (“System-level simulation results for channel vectorquantization feedback for MU-MIMO,” 3GPP TGS RAN WG1, R1-063028,November 2006) proposes a Fourier codebook construction that providesgood performance for line-of-sight channels or channels with a smallangle-of-spread. This codebook is constructed by extracting the top Mrows of a discrete Fourier transform (DFT) matrix of size P, where P isthe codebook size. A codeword is then selected from the codebook usingfeedback information provided by the mobile unit in response toinformation transmitted by the base station. However, the quantizationvalue indicated by a code word selected from the codebook is fixed oncetransmission to the mobile unit has been scheduled. The techniquedescribed by Philips does not permit the quantization value for ascheduled transmission by the mobile unit to be refined once it has beenselected. Thus, quantization values used by mobile units that arescheduled to transmit multiple frames cannot be modified by exploitingthe previous quantization vectors.

SUMMARY OF THE INVENTION

The present invention is directed to addressing the effects of one ormore of the problems set forth above. The following presents asimplified summary of the invention in order to provide a basicunderstanding of some aspects of the invention. This summary is not anexhaustive overview of the invention. It is not intended to identify keyor critical elements of the invention or to delineate the scope of theinvention. Its sole purpose is to present some concepts in a simplifiedform as a prelude to the more detailed description that is discussedlater.

In one embodiment of the present invention, a method is provided thatmay be implemented in a base station having a plurality of antennas andone or more user terminals. One embodiment of the method includesreceiving feedback from at least one user in response to transmitting afirst frame to said at least one user. The first frame is formed bypre-coding at least one symbol using at least one first code wordselected from at least one first code book associated with the at leastone user. The method also includes transmitting at least one secondframe to the user(s). The second frame(s) are pre-coded using at leastone second codeword selected from at least one second codebook. Thesecond codebook(s) determined based on the feedback and the firstcodeword(s).

Another embodiment of the method includes receiving, from the basestation, a first frame formed by pre-coding at least one symbol using afirst code word selected from a first code book associated with the userterminal. The method also includes transmitting information indicativeof a second codebook and at least one second codeword selected from thesecond codebook. The second codebook is determined based on the firstcodeword.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be understood by reference to the followingdescription taken in conjunction with the accompanying drawings, inwhich like reference numerals identify like elements, and in which:

FIG. 1 conceptually illustrates one exemplary embodiment of a wirelesscommunication system, in accordance with the present invention;

FIG. 2 conceptually illustrates one exemplary transition indicated byfeedback bits provided by the user, in accordance with the presentinvention;

FIG. 3 conceptually illustrates one exemplary set of transitionsindicated by feedback bits provided by the user, in accordance with thepresent invention;

FIG. 4 illustrates one exemplary embodiment of a discreet Fouriertransform-based hierarchical codebook construction, in accordance withthe present invention;

FIG. 5 compares the sum rate as a function of the signal-to-noise rationfor a rural macrocell propagation scenario (scenario D1 of WINNER) forN=1;

FIG. 6 compares the sum rate as a function of the signal-to-noise rationfor an indoor propagation scenario (scenario A1 of WINNER) for N=1.

While the invention is susceptible to various modifications andalternative forms, specific embodiments thereof have been shown by wayof example in the drawings and are herein described in detail. It shouldbe understood, however, that the description herein of specificembodiments is not intended to limit the invention to the particularforms disclosed, but on the contrary, the intention is to cover allmodifications, equivalents, and alternatives falling within the scope ofthe invention as defined by the appended claims.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Illustrative embodiments of the invention are described below. In theinterest of clarity, not all features of an actual implementation aredescribed in this specification. It will of course be appreciated thatin the development of any such actual embodiment, numerousimplementation-specific decisions should be made to achieve thedevelopers' specific goals, such as compliance with system-related andbusiness-related constraints, which will vary from one implementation toanother. Moreover, it will be appreciated that such a development effortmight be complex and time-consuming, but would nevertheless be a routineundertaking for those of ordinary skill in the art having the benefit ofthis disclosure.

Portions of the present invention and corresponding detailed descriptionare presented in terms of software, or algorithms and symbolicrepresentations of operations on data bits within a computer memory.These descriptions and representations are the ones by which those ofordinary skill in the art effectively convey the substance of their workto others of ordinary skill in the art. An algorithm, as the term isused here, and as it is used generally, is conceived to be aself-consistent sequence of steps leading to a desired result. The stepsare those requiring physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofoptical, electrical, or magnetic signals capable of being stored,transferred, combined, compared, and otherwise manipulated. It hasproven convenient at times, principally for reasons of common usage, torefer to these signals as bits, values, elements, symbols, characters,terms, numbers, or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise, or as is apparent from the discussion,terms such as “processing” or “computing” or “calculating” or“determining” or “displaying” or the like, refer to the action andprocesses of a computer system, or similar electronic computing device,that manipulates and transforms data represented as physical, electronicquantities within the computer system's registers and memories intoother data similarly represented as physical quantities within thecomputer system memories or registers or other such information storage,transmission or display devices.

Note also that the software implemented aspects of the invention aretypically encoded on some form of program storage medium or implementedover some type of transmission medium. The program storage medium may bemagnetic (e.g., a floppy disk or a hard drive) or optical (e.g., acompact disk read only memory, or “CD ROM”), and may be read only orrandom access. Similarly, the transmission medium may be twisted wirepairs, coaxial cable, optical fiber, or some other suitable transmissionmedium known to the art. The invention is not limited by these aspectsof any given implementation.

The present invention will now be described with reference to theattached figures. Various structures, systems and devices areschematically depicted in the drawings for purposes of explanation onlyand so as to not obscure the present invention with details that arewell known to those skilled in the art. Nevertheless, the attacheddrawings are included to describe and explain illustrative examples ofthe present invention. The words and phrases used herein should beunderstood and interpreted to have a meaning consistent with theunderstanding of those words and phrases by those skilled in therelevant art. No special definition of a term or phrase, i.e., adefinition that is different from the ordinary and customary meaning asunderstood by those skilled in the art, is intended to be implied byconsistent usage of the term or phrase herein. To the extent that a termor phrase is intended to have a special meaning, i.e., a meaning otherthan that understood by skilled artisans, such a special definition willbe expressly set forth in the specification in a definitional mannerthat directly and unequivocally provides the special definition for theterm or phrase.

FIG. 1 conceptually illustrates one exemplary embodiment of a wirelesscommunication system 100. In the illustrated embodiment, the wirelesscommunication system 100 includes a base station 105 that provideswireless connectivity to one or more users 110 (only one shown inFIG. 1) over corresponding air interfaces 115. However, persons ofordinary skill in the art having benefit of the present disclosureshould appreciate that the present invention is not limited to wirelesscommunication systems 100 that use base stations 105 to provide wirelessconnectivity. In alternative embodiments, the wireless communicationsystem 100 may use other devices to provide wireless connectivity, suchas base transceiver stations, base station routers, WiMAX or WiFi accesspoints, access networks, and the like. Techniques for establishing,maintaining, and operating air interfaces 115 to provide uplink and/ordownlink wireless communication links between the base station 105 andthe users 110 are known in the art and in the interest of clarity onlythose aspects of establishing, maintaining, and operating the airinterfaces 115 that are relevant to the present invention will bediscussed herein.

The base station 105 includes multiple antennas 120 for transmittingand/or receiving information over the air interfaces 115. Although threeantennas 120 are depicted in FIG. 1, persons of ordinary skill in theart having benefit of the present disclosure should appreciate that thebase station 105 is not limited to any particular number of antennas120. Moreover, persons of ordinary skill in the art having benefit ofthe present disclosure should appreciate that, in some embodiments, theusers 110 may also include multiple antennas. The base station 105 maytherefore employ multiple-input-multiple-output (MIMO) techniques sothat the multiple antennas 120 can transmit multiple independent anddistinct signals to the users 110 concurrently and on the same frequencyband using spatially multiplexed channels of the air interfaces 115.

In the illustrated embodiment, the base station 105 includes a precoder125 that maps signals to be transmitted to each user 110 onto theavailable channels using pre-coding matrices associated with the user110. The precoding matrix is generated based on the vector quantizationfeedback obtained from each user 110. The base station 105 may thereforestore code books 130 of quantization matrices, C_(i), associated witheach user 110 that is connected to the base station 105 In oneembodiment that includes a base station 105 having n_(T) antennas 120,the quantization matrices, C_(i) are n_(T)×n_(T) unitary pre-codingmatrices, i.e. satisfying CC^(H)=I. The quantization matrices, C_(i),stored in the codebooks 130 are defined so that they can be part of ahierarchical code book that includes multiple levels. The hierarchicalcodebook is organized such that each of the quantization matrices in arelatively low level are associated with one of the quantizationmatrices in the next higher level. The quantization matrices in arelatively high level are each associated with more than one of thequantization matrices in the next lower level. For example, thequantization matrices may be organized in a tree structure such thathigher-level quantization matrices are associated with multiple branchesthat indicate lower level pre-coding matrices. For example, thequantization matrices, C_(i), could be discrete Fourier transform (DFT)pre-coding matrices. However, persons of ordinary skill in the artshould appreciate that in alternative embodiments hierarchical codebookscan be organized in other ways.

The wireless communication system 100 utilizes a system model to definechannels between the base station 105 and the users 110. In theillustrated embodiment, the system model includes a narrowbandmulti-antenna downlink channel that is modeled as a MIMO-BC with flatfading. This model assumes that the base station 110 includes M transmitantennas 120 and K users 110 that are each equipped with N antennas. Thediscrete-time complex baseband signal received by the k-th user 110 is:

y _(k) =H _(k) x+n _(k); k=1, . . . , K

where H_(k)εC^(N×M) is the k-th user's channel matrix, xεC^(M×1) is thetransmitted signal vector, and each element of the complex additivewhite Gaussian noise at the user (n_(k)) is ≈CN(0,1). The transmittedsignal satisfies the sum-power constraint:

E[tr{xx^(H)}]≦P,

and the transmitted signal after pre-coding can be written as:

${x = {\sum\limits_{k = 1}^{S}{G_{k}d_{k}}}},$

where d_(k)=[d_(k,1), . . . , d_(k,|S) _(k) _(|)]^(T) is the |S_(k)|dimensional vector of symbols. The channel matrices are typically notperfectly known at the base station 105, but receivers at the users 110may be able to estimate the associated single-user channel matrix andmay be able to provide some amount of channel state information to thebase station on a finite-rate, approximately zero-delay, andapproximately error-free feedback channel. However, persons of ordinaryskill in the art having benefit of the present disclosure shouldappreciate that this model is an idealization and is not intended to bean exact representation of actual transmissions.

In operation, the base station 105 transmits pilot signals from eachantenna 120 over the air interfaces 115 to the user 110, which mayestimate the channels of the air interfaces 115 using the pilot signals.The user 110 may also calculate a channel direction indicator and/or achannel quality indicator. In one embodiment, the channel directionindicator includes information indicative of a codebook determined bythe user 110 and one or more codewords selected from this codebook. Theuser 110 may then provide feedback to the base station 105 includinginformation indicative of the channel detection indicator and/or thechannel quality indicator. The base station 105 may then use theprovided feedback to choose a set of users 110 to serve based on a sumrate criterion. The base station 105 may compute a pre-coding (orbeamforming) vector for each user 110 and use the pre-coding vector totransmit information, such as a frame, to each user 110.

Each user 110 may continue to provide feedback to the base station 105following the initial feedback provided in response to the pilot signal.The base station 105 may use the additional feedback provided by eachuser 110 to update the codewords and/or codebook associated with eachuser 110. In the illustrated embodiment, the feedback bits B provided byeach user 110 includes B_(i) bits, b_(l)=[b_(l) ⁽⁰⁾, . . . , b_(l) ^((B)^(l) ⁻¹⁾], which are used for updating the quantization codebook andB_(c) bits, b_(c)=[b_(c) ⁽⁰⁾, . . . , b_(c) ^((B) ^(cl) ⁻¹⁾], which areused for mapping the different codewords belonging to the same codebook.The total number of feedback bits is therefore: B=B_(l)+B_(c), whereP=2^(B) ^(c) and 2^(B) ^(l) ≧L. The codebooks should be constructed sothat the feedback provided by the users 110 is sufficient to synchronizethe codebooks maintained by the users 110 and the base station 105. Forexample, the code books associated with each user 110 may be part of ahierarchical codebook, e.g., each quantization codebook is a part of alevel l of a hierarchical codebook that has L levels, where 0≦l≦L, andthe bits may be used to indicate selected code words and/or code books.When the codebooks are modified or updated, the code words in each ofthe modified or updated codebooks should involve a possible improvementof the quantization quality. In one embodiment, the codebooks shouldalso be constructed so that a codeword chosen at the (l−1)-th level ofthe hierarchical codebook also belongs to an l-th level codebook.However, persons of ordinary skill in the art should appreciate that inalternative embodiments hierarchical codebooks could be organized inother ways.

In one embodiment, the hierarchical codebook is constructed based on aDFT quantization codebook. For example, let {tilde over (h)}εC^(M) bethe normalized channel vector (or channel direction) for a givenreceiver, after the receive combing stage. Let M be the number oftransmit antennas 120 and let K be the number of users 110 in the systemeach equipped with N antennas. The DFT matrix of dimension P is definedas:

$F_{P} = {\left\lbrack ^{{- j}\frac{2\pi \; {nm}}{P}} \right\rbrack_{n,{m = 0},\mspace{11mu} \ldots \mspace{11mu},{P - 1}}.}$

Supposing that P>M, the user 110 constructs a level 1 code book (e.g.,based on the pilot signals provided by the base station 105) using theformula:

${C_{k}^{(1)} = {{\left\{ \left\lbrack \frac{F_{P}}{\sqrt{M}} \right\rbrack_{{0:{M - 1}},q} \right\} q} = 0}},\ldots \mspace{11mu},{P - 1.}$

An initial code word is then selected from the level 1 code book basedon given maximization criterion

$\hat{h} = {\underset{c \in C_{k}^{(l)}}{\text{arg}\max}{d\left( {\overset{\sim}{h},c} \right)}}$

For example a minimum chordal distance criterion could be used. However,persons of ordinary skill in the art having benefit of the presentdisclosure should appreciate that other criteria may be used. The user110 may then transmit feedback bits representative of the selected codebook and/or code word to the base station 105, which may transmitinformation to the user 110 using pre-coding matrices determined basedon the feedback from the user 110 and any other users in the system 100.Following the initial feedback, the user 110 may continue to providefeedback bits to further refine or improve the pre-coding matricesselected by the base station 105.

FIG. 2 conceptually illustrates one exemplary transition indicated byfeedback bits provided by the user 110. The only possible transitionfrom the initial level 1 code book is from level 1 to level 2, and thistransition is indicated with a dotted arrow in FIG. 2. Since this is theonly possible transmission, the user 110 only provides the B_(c)feedback bits for mapping ĥ⁽¹⁾ and does not transmit bits for mapping tothe new level. The transmission of the B_(c) feedback bits is indicatedwith a solid arrow in FIG. 2.

FIG. 3 conceptually illustrates one exemplary set of transitionsindicated by feedback bits provided by the user 110. In the illustratedembodiment, the user 110 has previously transitioned to a code book atquantization level l. The user 110 checks to determine whether thesequence ĥ⁽¹⁾, . . . , ĥ^((l−1)) of previous selected codewords is stilloptimum given the sequence of generated codebooks C⁽¹⁾, . . . ,C^((l−1)). This check helps the user 110 to track channel variations. Ifa different value is found at the l th level, then a new value forĥ^((l)) is generated. The new value for ĥ^((l)) is communicated to thebase station 105 using the B_(c) bits and the value of l is communicatedto the transmitter by using the B_(l) bits. The level to be used at thenext step is set to l+1, and this indicated in FIG. 3 below by using adashed arrow. If the user 110 determines that the previous sequence ofselected codewords is still optimum, a new codebook is generated asfollows:

${C^{(l)} = {{\left\{ \left\lbrack \frac{F_{P^{l}}}{\sqrt{M}} \right\rbrack_{{0:{M - 1}},{{({{w^{({l - 1})}P} + q})}\text{mod}P}} \right\} q} = {- \frac{P}{2}}}},\ldots \mspace{11mu},\frac{P}{2},$

where w^((l−1)) is the index of ĥ^((l−1)) in C^((l)). The user 110 thenselects the l-th level code word from the new code book using a givenmaximization criterion:

${\hat{h}}^{(l)} = {\underset{c \in C_{k}^{(l)}}{\text{arg}\max}{d\left( {\overset{\sim}{h},c} \right)}}$

For example the minimum chordal distance criterion could be used.However, persons of ordinary skill in the art having benefit of thepresent disclosure should appreciate that other criteria may be used.This value is communicated to the transmitter by using the B_(c) bits,whereas the value of l+1 is communicated to the transmitter by using theB_(l) bits.

The user 110 also has the option of performing a backward step to ahigher level, as indicated by the dotted arrows in FIG. 3. For example,since the channel vector is typically time variable, the preferredcodebook may be found among higher levels in a previously exploredsubtree of the hierarchical codebook. The user 110 may elect to performa backward step to the next higher level (l−1), e.g., in cases whereslow fading causes relatively small changes in the channels.Alternatively, the user 110 may elect to perform a backward step to acodebook that is more than one level higher than the current codebook,e.g., in cases where fast fading causes relatively large variations inthe channels

FIG. 4 illustrates one exemplary embodiment of a discreet Fouriertransform-based hierarchical codebook construction. In the illustratedembodiment, P=2, M−2, and L=3. At each level the codewords are selectedfrom the sub matrix obtained from the DFT by considering only the firstM rows. The codewords of the l-th level codebook are denoted byrectangles. The sequence of “best” codewords is denoted by the boldrectangles.

The closed-loop beamforming techniques described herein may have anumber of advantages over conventional practice. Under ideal conditionsof perfect channel knowledge at the transmitter, conventional andadvanced beamforming techniques promise significant performance gainscompared to single-antenna transmission techniques. The techniquesdescribed herein may approach ideal beamforming performance in a simple,practical manner. For a given level of complexity, the proposedhierarchical technique has been shown to outperform conventionalnon-hierarchical techniques, particularly in cases where the channel isslowly changing, such as fixed wireless systems. Under these conditions,the hierarchical technique is especially efficient for achievingnear-ideal beamforming performance. The techniques described herein maybe implemented in any system using beamforming based on limited channelstate feedback, including all next-generation cellular standardsincluding LTE, UMB, 802.16e, and 802.16m.

The link performance of the proposed technique may be compared with theFourier codebook and RVQ techniques for a spatial channel model (SCM)with M=4 antennas at the transmit side, N=1,2 antennas at the receiveside, 0.5 wavelength element spacing both at the base and at each user,K=10 users. The channel is considered perfectly estimated at the receiveside. FIG. 5 compares the sum rate as a function of the signal-to-noiseratio for a rural macrocell propagation scenario (scenario D1 of WINNER)for N=1. FIG. 6 compares the sum rate as a function of thesignal-to-noise ration for an indoor propagation scenario (scenario A1of WINNER) for N=1. The proposed scheme has been implemented for B=3 (2quantization stages) and B=4 (3 quantization stages). The proposedhierarchical technique obtains the same performance as the Fouriercodebook with a lower number of feedback bits. Moreover, the proposedscheme clearly outperforms the RVQ techniques. The hierarchical approachalso reduces the computational load at the receive side.

The particular embodiments disclosed above are illustrative only, as theinvention may be modified and practiced in different but equivalentmanners apparent to those skilled in the art having the benefit of theteachings herein. Furthermore, no limitations are intended to thedetails of construction or design herein shown, other than as describedin the claims below. It is therefore evident that the particularembodiments disclosed above may be altered or modified and all suchvariations are considered within the scope of the invention.Accordingly, the protection sought herein is as set forth in the claimsbelow.

1. A method implemented in a base station having a plurality ofantennas, comprising: receiving feedback from at least one user inresponse to transmitting a first frame to said at least one user, thefirst frame formed by pre-coding at least one symbol using at least onefirst code word selected from at least one first code book associatedwith said at least one user; transmitting at least one second frame tosaid at least one user, said at least one second frame being pre-codedusing at least one second codeword selected from at least one secondcodebook, said at least one second codebook being determined based onthe feedback and said at least one first codeword.
 2. The method ofclaim 1, comprising associating said at least one user with said atleast one first code word selected from said at least one first codebook.
 3. The method of claim 2, wherein associating said at least oneuser with said at least one first codeword selected from said at leastone first codebook comprises: transmitting a plurality of pilot signalsfrom the plurality of antennas; receiving information indicative of saidat least one first code word and said at least one first code book fromsaid at least one user in response to transmitting the plurality ofpilot signals; and selecting said at least one user based on a sumweight criterion.
 4. The method of claim 1, wherein receiving feedbackfrom said at least one user comprises receiving information indicativeof said at least one second codeword and said at least one secondcodebook, said at least one first code book and said at least one secondcodebook being different levels in a hierarchy of codebooks, the firstand second codebooks comprising first and second pluralities of discreteFourier transform matrices, respectively.
 5. The method of claim 4,wherein receiving feedback from said at least one user comprisesreceiving information indicative of said at least one second codewordand said at least one second codebook, said at least one second codebookbeing at a lower level than said at least one first codebook and said atleast one second codebook being defined so that said at least one firstcodeword is in said at least one second codebook.
 6. The method of claim4, wherein receiving feedback from said at least one user comprisesreceiving information indicative of said at least one second codewordand said at least one second codebook, said at least one second codebookbeing at a higher level than said at least one first codebook.
 7. Themethod of claim 1, wherein receiving feedback from said at least oneuser comprises receiving a plurality of bits indicative of said at leastone second code word and said at least one second codebook.
 8. A methodimplemented in user terminal configured to communicate with a basestation having a plurality of antennas, comprising: receiving, from thebase station, a first frame formed by pre-coding at least one symbolusing a first code word selected from a first code book associated withthe user terminal; transmitting information indicative of a secondcodebook and at least one second codeword selected from the secondcodebook, the second codebook being determined based on the firstcodeword.
 9. The method of claim 8, comprising forming the secondcodebook based on the first codeword.
 10. The method of claim 9, whereinforming the second codebook based on the first codeword, comprises:receiving a plurality of pilot signals from the plurality of antennas;and forming the second codebook based on the first codeword and theplurality of pilot signals.
 11. The method of claim 9, wherein formingthe second codebook comprises forming the second codebook such that thefirst code book and the second codebook represent different levels in ahierarchy of codebooks, the first and second codebooks comprising firstand second pluralities of discrete Fourier transform matrices,respectively.
 12. The method of claim 11, wherein forming the secondcodebook comprises forming the second codebook such that the secondcodebook is at a lower level than the first codebook and said at leastone first codeword is in the second codebook.
 13. The method of claim11, wherein forming the second codebook comprises forming the secondcodebook such that the second codebook is at a higher level than thefirst codebook.
 14. The method of claim 8, comprising selecting said atleast one second codeword from a second codebook that is at a higherlevel in a hierarchical codebook than the first codebook.
 15. The methodof claim 14, wherein selecting said at least one second codeword fromthe second codebook at the higher levels in the hierarchical codebookcomprises selecting said at least one second codeword from a previouslyformed second codebook.
 16. The method of claim 8, wherein transmittinginformation indicative of the second codebook and said at least onesecond codeword comprises transmitting a plurality of bits indicative ofsaid at least one second code word and the second codebook.
 17. Themethod of claim 8, comprising receiving, from the base station, at leastone second frame that was pre-coded using said at least one secondcodeword selected from the second codebook.